Collins functions for pions from SIDIS and newe+e−data: A first glance at their transverse momentum dependence

New data from the BABAR Collaboration, on azimuthal asymmetries measured in ${e}^{+}{e}^{\ensuremath{-}}$ annihilations into pion pairs at ${Q}^{2}=112\text{ }\text{ }{\mathrm{GeV}}^{2}$, allow us to take the first, direct glance at the ${p}_{\ensuremath{\perp}}$ dependence of the Collins functions, in addition to their $z$ dependence. These data, together with previous ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}_{1}{h}_{2}$ Belle measurements and the available semi-inclusive deep in